[FRIAM] Can empirical discoveries be mathematical?

Fri Sep 3 15:15:53 EDT 2021

It doesn't take much observing to realize that rotations of an object in 3D
are not commutative.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Sep 3, 2021, 12:41 PM Russ Abbott <russ.abbott at gmail.com> wrote:

> I would guess that most mathematical discoveries are first encountered
> empirically. Then the mathematician who encounters it attempts to prove the
> observed phenomenon mathematically. Your bachelor example illustrates. Once
> you discovered the apparent phenomenon that all unmarried men are
> bachelors -- and as you also noticed that all bachelors are unmarried --
> you proved that the two collections are identical by determining that
> that's how bachelor is defined, a mathematical relationship. Will you be
> writing up and submitting this result to a mathematics journal -- rather
> than, for example, to a journal of sociology?
>
> -- Russ Abbott
> Professor Emeritus, Computer Science
> California State University, Los Angeles
>
>
> On Fri, Sep 3, 2021 at 11:09 AM Pieter Steenekamp <
> pieters at randcontrols.co.za> wrote:
>
>> Eric,
>>
>> Nick's question and the parsing of discoveries into two types intrigue
>> me. I'm an engineer, so maybe I have a deep seeded philosophy of science
>> envy?
>>
>> Pieter
>>
>> On Fri, 3 Sept 2021 at 19:58, Eric Charles <
>> eric.phillip.charles at gmail.com> wrote:
>>
>>> Why are we parsing discoveries into those two types?
>>>
>>> I think traditionally,  "mathematical" would have been synonymous with
>>> "rigorous deduction groin a minimal number of axioms", but I doubt that
>>> approach is clear cut anymore.
>>>
>>> Given that you claim to have sussed out your insight via systematic
>>> *empirical* observation,  and you claim it regarding a particular class
>>> of *empirical* objects... I'd go with "empirical"... if I had to choose
>>> one for you... but I'm also not sure why we would play this game to begin
>>> with.
>>>
>>> Unless you confessed to me that it was insecurities tied to a deep
>>> seeded physics envy... in which case I'd at least understand why you
>>> asked.
>>>
>>> On Fri, Sep 3, 2021, 1:25 PM <thompnickson2 at gmail.com> wrote:
>>>
>>>> By discovery, I mean only happening on a regularity that was unexpected.
>>>>
>>>>
>>>>
>>>> I guess I didn’t need all the razzle-dazzle about the t-shirts.  Let’s
>>>> say that I, being totally naïve of logic, announced to friam that I had
>>>> made a survey of all my never-married male friends and each and every one
>>>> claimed to be a bachelor.  I offered to you-all, as an insight, that all
>>>> unmarried men are bachelors.   I think I have made that “discovery”
>>>> empirically; you might have arrived at the same insight logically.  Perhaps
>>>> the empirical vs mathematical thing is methodological.  Of course, I now
>>>> realize that inorder to arrive at my empirical conclusion, I had to invoke
>>>> the logical form, induction: this man is un-married, this man is a
>>>> batchelor, all batchelors are unmarried.  You might have arrived at the
>>>> same conclusion deductively (i.e., mathematically).
>>>>
>>>>
>>>>
>>>> Nick Thompson
>>>>
>>>> ThompNickSon2 at gmail.com
>>>>
>>>> https://wordpress.clarku.edu/nthompson/
>>>>
>>>>
>>>>
>>>> *From:* Friam <friam-bounces at redfish.com> *On Behalf Of *Pieter
>>>> Steenekamp
>>>> *Sent:* Friday, September 3, 2021 12:48 PM
>>>> *To:* The Friday Morning Applied Complexity Coffee Group <
>>>> friam at redfish.com>
>>>> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>>>>
>>>>
>>>>
>>>> Nick,
>>>>
>>>> I quote from https://www.britannica.com/science/scientific-theory
>>>>
>>>> "In attempting to explain objects and events, the scientist employs (1)
>>>> careful observation or experiments, (2) reports of regularities, and (3)
>>>> systematic explanatory schemes (theories). The statements of regularities,
>>>> if accurate, may be taken as empirical laws expressing continuing
>>>> relationships among the objects or characteristics observed."
>>>>
>>>> Based on this, I reckon, because you have reported the regularities,
>>>> you have discovered an empirical scientific law. Congratulations!
>>>>
>>>> Next is to systematically explain it, then you have a scientific theory!
>>>>
>>>> Maybe I did not answer your question? You asked if this is an empirical
>>>> discovery or a mathematical one.
>>>>
>>>>
>>>> IMO you have done only the first part, the empirical discovery. This
>>>> could now be taken further and if you can prove it using formal
>>>> mathematics, then only can you claim you have made a mathematical
>>>> discovery. So, it is (not yet) a mathematical discovery. Sorry to blow your
>>>> bubble.
>>>>
>>>> P
>>>>
>>>>
>>>>
>>>> On Fri, 3 Sept 2021 at 17:24, <thompnickson2 at gmail.com> wrote:
>>>>
>>>> Colleagues,
>>>>
>>>>
>>>>
>>>> Years ago, my daughter, who knows I hate to shop, bought me a bunch of
>>>> plain T-shirts.  The label’s on the shirts were printed, rather than
>>>> attached, and so have faded.  Each morning, this leaves me with the problem
>>>> of decerning which is the front and which the back of the shirt, and even,
>>>> which the inside and which the out-.  After years of fussing with these
>>>> shirts I decerned a pattern.  Up/down, inside-in/inside-out, left/right,
>>>> front/back, crossed arms/uncrossed arms, you can’t do one transformation
>>>> without doing at least one other.
>>>>
>>>>
>>>>
>>>> Is this an empirical discovery or a mathematical one?
>>>>
>>>>
>>>>
>>>> I guess it boils down to whether “front/back” entails in its meaning
>>>> another transformation.   Should we call empirical discoveries
>>>> “discoveries” and mathematical discoveries “revelations”?
>>>>
>>>>
>>>>
>>>> Nick
>>>>
>>>>
>>>>
>>>> Nick Thompson
>>>>
>>>> ThompNickSon2 at gmail.com
>>>>
>>>> https://wordpress.clarku.edu/nthompson/
>>>>
>>>>
>>>>
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